Article
force could be adjusted to reach the desired depth level, if necessary.
The scan progressed until all pixels in the design were patterned into the
surface, at which point the tip was available to write the next pattern.
To obtain Ag diffractive surfaces, Ag was thermally evaporated^43
(Kurt J. Lesker, Nano36) onto the patterned polymer film at a pres-
sure of about 3 × 10−7 mbar. A tungsten boat loaded with Ag pellets was
heated to deposit at a rate of 25 Å s−1. The process was stopped when the
film thickness was around 750 nm. A glass slide was then affixed with
ultraviolet-curable epoxy (OG142-95) onto the exposed Ag surface,
and the glass/epoxy/Ag stack peeled off, revealing a Ag surface with
the negative of the initial pattern in the polymer surface.
SiNx surfaces were obtained by using a Si/SiO 2 /SiNx stack as a sub-
strate. A layer of SiO 2 2,000 nm thick was thermally grown onto a
Si wafer, followed by chemical vapour deposition of a layer of SiNx
200 nm thick. The wafer was diced into 1.5 cm × 1.5 cm pieces for ther-
mal scanning-probe lithography using PMMA/MA as the polymer.
The pattern in the polymer film was transferred into the underlying
SiNx substrate via reactive-ion etching (Oxford Instruments, NPG 80)
using a gas mixture of 50 standard cubic centimetres per minute (sccm)
CHF 3 and 5 sccm O 2. The etching was performed at a chamber pressure
of 55 mTorr, with 100 W radio-frequency power and a SiNx etch rate of
45 nm min−1 for 5 min, where the depth of the transferred pattern in
SiNx was approximately the same as the depth in the polymer pattern
(approximately 1:1 selectivity). Afterwards, the substrate was ultra-
sonicated in acetone, followed by isopropanol, and blown dry with N 2.
To obtain Si surfaces for either direct use or for templating, the pat-
tern in the polymer film was transferred into the underlying Si substrate
via inductively coupled plasma etching (Oxford Instruments, Plasma
Pro) using a gas mixture of 17.0 sccm SF 6 , 17.5 sccm C 4 F 8 and 60 sccm
Ar. The Si etching was done at a chamber pressure of 20 mTorr, with a
forward power of 50 W, and at a rate of ~25 nm min−1 for 6.33 min, where
the depth of the transferred pattern in Si was approximately the same
as the depth in the polymer pattern (approximately 1:1 selectivity).
After etching, the sample was sonicated for 2 min in acetone and 2 min
in IPA, followed by 5 min of O 2 plasma cleaning at 600 W.
Patterned TiO 2 samples were obtained by using patterned Si tem-
plates. A 25-nm-thick Au layer was thermally evaporated onto the
patterned Si wafer at a pressure of approximately 3 × 10−7 mbar and
a rate of 10 Å s−1. TiO 2 was then radio-frequency-sputtered onto the
exposed gold surface (von Ardenne, CS 320 S) with 400 W, a chamber
pressure of 4 × 10−3 mbar, and 14 sccm Ar, for 160 min, resulting in an
approximately 300-nm-thick film. A glass slide was then affixed with
ultraviolet-curable epoxy (OG116-31) onto the exposed TiO 2 layer, and
the glass/epoxy/TiO 2 /Au stack peeled off, revealing a TiO 2 /Au surface
with the negative of the initial pattern in the Si surface. Finally, the Au
layer was removed by immersing the sample in aqua regia (4:1 mixture
of HCl:HNO 3 ) for 5 min. Afterwards, the sample was rinsed in deionized
water and blown dry with N 2.
Binarized-surface design and fabrication
For each Fourier surface in Fig. 1 with height profile f(x) (see Extended
Data Table 1), a binarized version was fabricated by electron-beam
lithography and etching, followed by templating (see Extended Data
Fig. 4). The binarization followed a published thresholding procedure^44.
This required the electron-beam lithography resist to be exposed
wherever fx()+<Δ 0. The Si substrate was then etched in these
locations.
To prepare the samples, 2 × 2 cm chips (diced from a 4-inch-diameter,
1-mm-thick Si wafer) were cleaned by sonicating for 2 min in acetone
and 2 min in IPA, followed by 5 min of O 2 plasma cleaning at 600 W.
CSAR (electron-beam lithography resist) was deposited on the sam-
ple surfaces and accelerated at 500 rpm s−1 to 500 rpm for 5 s in a first
spin-coating step. In a second step, the samples were accelerated at
2,000 rpm s−1 to 2,000 rpm for a total time of 40 s. After spin-coating,
the samples were baked at 150 °C for 1 min. The samples were then
loaded into an electron-beam lithography system (Vistec, NFL 5) and
patterned by exposing the resist layer where specified by the thresh-
olding procedure^44. After exposure, the samples were developed in AR
600-546 for 1 min, and subsequently rinsed in IPA. The patterns were
etched to depths approximately matching that of the correspond-
ing Fourier surfaces from Fig. 1 with HBr-based reactive-ion etching
(Oxford, Plasmalab System 100). The Si etching was done using 40 sccm
HBr at a chamber pressure of 3 mTorr, with a forward power of 200 W,
radio-frequency power of 20 W, and at a rate of approximately 30 nm
min−1 for 2 min. After etching, the resist was removed by subsequent
sonication in acetone and in IPA, followed by 2 min of O 2 plasma cleaning
at 600 W, a dip in buffered hydrofluoric acid (1:7 mixture of AF 875-125
and H 2 O), and rinsing with H 2 O. The samples were cleaned in piranha
(1:1 mixture of H 2 SO 4 :H 2 O 2 ) for 15 min, ultrasonicated in H 2 O and in IPA,
and blown dry with N 2. (Caution: care should be taken with piranha as
it reacts violently with solvents and other organic materials.) These
binarized surfaces were then replicated in Ag using the same procedure
as for the Fourier surfaces.Surface-topography characterization
The topography of the Fourier surfaces was measured by the scanning
probe during patterning and independently verified with AFM on the
templated Ag surface. The topography of our Ag single-sinusoidal
surface (Fig. 1a, b) is analysed in Extended Data Fig. 2. AFM scans (Bruker,
Dimension FastScan AFM with a Bruker NCHV-A cantilever) were col-
lected in tapping mode under ambient conditions. The raw data was
processed by first removing the instrumental high-frequency scan noise
in the scanning-probe analysis software Gwyddion (version 2.54, http://
gwyddion.net). Next, row alignment and plane-levelling were performed
in MATLAB (version 2019a, http://ch.mathworks.com/products/matlab.
html) to obtain the corrected data, shown in Extended Data Fig. 2a.
These data were then analysed by fitting a sinusoidal function (with
the form shown in Extended Data Table 1 for Fig. 1a; periodic along x,
constant in y), where the fit parameters and residuals were extracted.
The amplitude and period of the fitted function were A 1 = 25.5 nm
(2% larger than design value) and Λ = 610 nm (1.7% larger than design
value), respectively. As we obtained a consistent horizontal distance
error in both our etched and templated gratings, we attributed this
error to a distance miscalibration in the thermal scanning probe. The
RMS error between the design function and measured topography for
the structure in Fig. 1a was found to be 1.8 nm after this error was taken
into account. A similar procedure was used to extract RMS errors for
other Fourier surfaces, as reported in the legends of Fig. 1 and Extended
Data Fig. 9. See Extended Data Fig. 2 for further details. For the photonic
diffraction gratings in Extended Data Fig. 8, a slight nonlinearity in the
patterning of deeper structures was also taken into account.Optical characterization
The optical-characterization setup is depicted in Extended Data Fig. 3a.
Ag surfaces were measured with an inverted optical microscope (Nikon,
Eclipse Ti-U) equipped with a 50× air objective (Nikon, TU Plan Fluor,
numerical aperture NA = 0.8). A halogen lamp was used to illuminate
the sample. The lamp filament was imaged onto the back focal plane of
the microscope objective. After a beamsplitter, the light was focused
onto the sample and then collected by the same objective. Reflected
light was transmitted through the beamsplitter and passed through a
circular aperture in the real-space image plane to isolate the structure
of interest. The back focal plane was imaged onto the entrance slit of an
imaging spectrograph (Andor Shamrock 303i) where it was relayed to
a sensitive digital camera (Andor Zyla PLUS sCMOS) for image acqui-
sition. Reflectivity measurements were obtained for both dispersed
k-space measurements (Fig. 1c, f, i, Extended Data Fig. 4b, d, f, Extended
Data Fig. 5b and Extended Data Fig. 6b–i) and k-space images (Fig. 2c, d
and Fig. 3c, f), by acquiring a background image, a reference image
and a signal image. The background, reference and signal images were